Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Prospective bounds on f(Q) gravity with pulsar timing arrays

Mohammadreza Davari, Alireza Allahyari

TL;DR

This work assesses symmetric teleparallel $f(Q)$ gravity as a non-metricity-based modification to GR using pulsar timing arrays. By adopting a model-independent damping parameter for tensor modes and deriving an analytic transfer function, the authors connect inflationary GWs to PTA observables while enforcing GW speed equal to light speed ($c_T=1$). Using NANOGrav 15-year and IPTA2 data, they find $n$ consistent with GR within uncertainties, though small deviations remain possible. Fisher-forecast analyses for the SKA indicate that future PTAs could constrain $n$ to the level of $\mathcal{O}(10^{-5})$, sharply testing $f(Q)$ gravity against GR. Overall, PTAs emerge as powerful probes of non-metricity modifications to gravity with strong potential for future discovery.

Abstract

Pulsar timing arrays (PTAs) have recently provided compelling evidence for a stochastic gravitational wave background (SGWB) in the nanohertz frequency band, offering a unique window into fundamental physics. Here, we explore implications for symmetric teleparallel $f(Q)$ gravity, a theory in which deviations from General Relativity (GR) arise through the non-metricity scalar $f(Q)$. Crucially, tensor modes propagate at the speed of light in this framework. However, their amplitude undergoes a modified damping during their evolution. We adopt a model-independent parameterization and derive an analytic approximation to the tensor mode transfer function to obtain the spectral energy density of primordial inflationary gravitational waves. Comparison with the NANOGrav 15-year and IPTA second data releases show that the inferred damping parameter $n$ remains consistent with GR, yet allows small deviations that could be observable. We then conduct a Fisher information matrix forecasts which demonstrate that the Square Kilometre Array (SKA) observatory will improve these constraints by several orders of magnitude, offering the potential to distinguish $f(Q)$ gravity from GR with high precision. These results highlight PTAs as powerful probes of non-metricity-based modifications to gravity.

Prospective bounds on f(Q) gravity with pulsar timing arrays

TL;DR

This work assesses symmetric teleparallel gravity as a non-metricity-based modification to GR using pulsar timing arrays. By adopting a model-independent damping parameter for tensor modes and deriving an analytic transfer function, the authors connect inflationary GWs to PTA observables while enforcing GW speed equal to light speed (). Using NANOGrav 15-year and IPTA2 data, they find consistent with GR within uncertainties, though small deviations remain possible. Fisher-forecast analyses for the SKA indicate that future PTAs could constrain to the level of , sharply testing gravity against GR. Overall, PTAs emerge as powerful probes of non-metricity modifications to gravity with strong potential for future discovery.

Abstract

Pulsar timing arrays (PTAs) have recently provided compelling evidence for a stochastic gravitational wave background (SGWB) in the nanohertz frequency band, offering a unique window into fundamental physics. Here, we explore implications for symmetric teleparallel gravity, a theory in which deviations from General Relativity (GR) arise through the non-metricity scalar . Crucially, tensor modes propagate at the speed of light in this framework. However, their amplitude undergoes a modified damping during their evolution. We adopt a model-independent parameterization and derive an analytic approximation to the tensor mode transfer function to obtain the spectral energy density of primordial inflationary gravitational waves. Comparison with the NANOGrav 15-year and IPTA second data releases show that the inferred damping parameter remains consistent with GR, yet allows small deviations that could be observable. We then conduct a Fisher information matrix forecasts which demonstrate that the Square Kilometre Array (SKA) observatory will improve these constraints by several orders of magnitude, offering the potential to distinguish gravity from GR with high precision. These results highlight PTAs as powerful probes of non-metricity-based modifications to gravity.
Paper Structure (7 sections, 34 equations, 4 figures, 3 tables)

This paper contains 7 sections, 34 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Primordial GWs
  3. GWs in $f(Q)$ gravity
  4. Bounds by PTAs
  5. NANOGrav and IPTA
  6. SKA observatory
  7. Summary and discussion

Figures (4)

  • Figure 1: The posterior plots and marginal posteriors of $f(Q)$ gravity parameters with $\text{log}_{10}A = -14.2$. The contours show at 68% and 95% confidence levels for International PTA second data release (IPTA2) in blue and NANOGrav 15-year data set (NG15) in green.
  • Figure 2: The current spectral energy density of GWs as a function of frequency in logarithmic scales for $f(Q)$ model. The violin plots show NANOGrav 15-year data set (NG15) and International PTA second data release (IPTA2).
  • Figure 3: The gravitational wave signal spectrum from $f(Q)$ gravity (green) compared to the SKA noise spectrum (pink).
  • Figure 4: The posterior plots and marginal posteriors of the parameters. The contours show at 68% and 95% confidence levels for two scenarios SKA (normal) in indigo and SKA (optimistic) in emerald.